Should a person called to the Torah for the reading of the 10 commandments from Parasha Yitro be Shomrei Shabbat?
It is not suitable at any time to call to the Torah someone who is not Shomer Torah Umitzvot. All the more, when referring to special and respectable Aliyot (like the 10 commandments), it disrespects the Tzibur and the Torah to call up someone as such. However, any Jew can be called to the Torah, but on Shabbat one has to have seven people who are Shomer Torah Umitzvot called up. After having called up seven people, one may add others. The Mishna Berura writes that one should not give a person who is suspected for not keeping a certain Mitzva an Aliya that includes such a Mitzva (as Shabbat or Arayot). Rabbi Ro'i Margalit